MCNP Guide

❮ Tutorial: Criticality AnalysisVariance Reduction ❯

Tutorial: Shielding Analysis

Practical radiation shielding calculation with MCNP

Problem Setup

We'll model a practical shielding problem: a 14 MeV neutron source behind a composite steel and concrete shield.

Physical Setup

  • 14 MeV neutron point source (D-T fusion)
  • 2 cm steel liner (gamma shielding)
  • 30 cm concrete shield (neutron moderation)
  • Detector points at 50 cm and 100 cm

Analysis Goals

  • Calculate neutron flux attenuation
  • Determine dose rates at detector points
  • Evaluate shield effectiveness
  • Use variance reduction for deep penetration

Complete Input File

This input demonstrates a complete shielding analysis with multiple tallies and variance reduction.

mcnp
Neutron Shielding Analysis Example
c Cell Cards
1  0        -1      imp:n=1    $ Source region
2  2  -7.85  1 -2   imp:n=2    $ Steel liner
3  3  -2.3   2 -3   imp:n=4    $ Concrete shield
4  0         3 -4   imp:n=2    $ Detector region
5  0         4      imp:n=0    $ Outside world

c Surface Cards
1  so   0.5      $ Source sphere
2  px   2.0      $ Steel back face
3  px   32.0     $ Concrete back face
4  px   132.0    $ Problem boundary

c Data Cards
c Materials
m2  26056.70c  -1.0       $ Steel (simplified)
m3  1001.70c   -0.01      $ Concrete
    8016.70c   -0.532
    14028.70c  -0.337
    20040.70c  -0.044
    26056.70c  -0.014
    13027.70c  -0.034
    11023.70c  -0.029

c Source - 14 MeV neutron point source
sdef  par=n  erg=14  pos=0 0 0

c Tallies
f2:n  1 2 3 4               $ Surface flux
e2    1e-9 1e-6 1e-3 0.1 1 5 10 15
f5:n  50 0 0  0             $ Point detectors
      100 0 0  0
e5    1e-9 1e-6 1e-3 0.1 1 5 10 15
f4:n  2 3                   $ Cell flux

c Physics and cutoffs
mode  n                     $ Neutron transport only
cut:n 1e-8                  $ Energy cutoff
nps   1e6                   $ Number of particles

Key Features Explained

Geometry and Materials

The geometry uses simple spherical and planar surfaces for clarity. Materials are simplified but representative.

  • Steel (m2): High-density material for gamma attenuation
  • Concrete (m3): Hydrogen-rich material for neutron moderation
  • Importance: Increases through shield (1→2→4) to maintain statistics

Tally Strategy

  • F2: Surface flux shows attenuation through each layer
  • F5: Point detectors give precise flux at specific locations
  • F4: Cell flux in each shield layer (post-process for dose)
  • Energy bins: Track spectrum changes from thermal to 14 MeV

Variance Reduction

Shielding problems require variance reduction to keep tally relative errors reasonable in deep penetration regions. The base input already increases neutron importance through the shield (1 → 2 → 4 → 2 → 0). To further accelerate convergence you can add DXTRAN spheres, weight windows, or point detectors.

Enhanced Input with DXTRAN Sphere

mcnp
c Add to the previous input:
c Variance reduction
dxtran   0 0 0  40.0        $ Sphere radius 40 cm
cut:n   1e-8
nps     5e5

Running and Analysis

Running the Calculation

bash
# Run the shielding calculation
mcnp6 i=shield_input n=shield_output

# Monitor progress
tail -f shield_output

# Check for completion
grep "mcnp     version" shield_output

Key Results to Extract

  • Attenuation factors: Compare F2 tallies across surfaces
  • Dose rates: F5 results with flux-to-dose conversion
  • Energy spectra: How neutron spectrum changes through shield
  • Statistical quality: Verify all tallies pass statistical tests

Interpreting Results

Typical Results

  • Steel reduces flux by factor of ~2 (mainly fast neutrons)
  • Concrete reduces flux by factor of ~100-1000 (depends on thickness)
  • Thermal neutron flux increases in concrete (moderation)
  • Fast neutron flux decreases exponentially with depth

Shielding Analysis Tips

  • Always use variance reduction for deep penetration problems
  • Check that statistical tests pass for all tallies
  • Compare results to analytical estimates when possible
  • Consider both neutron and gamma shielding requirements
  • Use appropriate flux-to-dose conversion factors

Extensions and Variations

Geometry Variations

  • Add air gaps between materials
  • Include reinforcing steel in concrete
  • Model realistic source geometry
  • Add streaming paths (ducts, penetrations)

Physics Enhancements

  • Include photon transport (mode n p)
  • Add activation calculations
  • Consider thermal scattering in concrete
  • Use detailed material compositions

Learning Objectives

After completing this tutorial, you should be able to:

  • Set up a multi-layer shielding problem
  • Apply appropriate variance reduction techniques
  • Use multiple tally types for comprehensive analysis
  • Interpret shielding effectiveness results
  • Understand the physics of neutron attenuation

Related Topics

❮ Tutorial: Criticality AnalysisVariance Reduction ❯